Adjustable cross-frame assembly and method of use thereof

ABSTRACT

An adjustable cross-frame assembly includes a first elongate flexible line, a second elongate flexible line, and an adjustable-length jack assembly. The first elongate flexible line is coupled in tension to a first portion of a first girder and to a second portion of a second girder. The first elongate flexible line extends concurrently with a plane that intersects both of the first and second girders. The second elongate flexible line is coupled in tension to a second portion of the first girder and to a second portion of the second girder. The second elongate flexible line extends concurrently with the plane. The adjustable-length jack assembly is coupled to the first portion of the first girder and to the second portion of the second girder. The adjustable-length jack assembly extends concurrently with the plane.

RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application No. 63/367,065, filed, Jun. 27, 2022, the entire content of which is hereby incorporated by reference.

GOVERNMENT LICENSE RIGHTS

This invention was made with government support under the Innovation Deserving Exploratory Analysis (IDEA) Program awarded by the Transportation Research Board of the National Academies of Sciences, Engineering, and Medicine. The government has certain rights in the invention.

FIELD

Embodiments described herein relate to the installation of cross-frames between girders of a structure, such as a bridge or overpass.

SUMMARY

In one aspect, embodiments disclosed herein relate to an adjustable cross-frame assembly includes a first elongate flexible line, a second elongate flexible line, and an adjustable-length jack assembly. The first elongate flexible line is coupled in tension to a first portion of a first girder and to a first portion of a second girder. The first elongate flexible line extends in a direction approximately parallel with a plane that intersects both of the first and second girders. The second elongate flexible line is coupled in tension to a second portion of the first girder and to a second portion of the second girder. The second elongate flexible line extends in a direction approximately parallel with the plane. The adjustable-length jack assembly is coupled to the first portion of the first girder and to the second portion of the second girder. The adjustable-length jack assembly extends in a direction approximately parallel with the plane.

In another aspect, embodiments disclosed herein relate to an adjustable cross-frame assembly to facilitate the installation of cross-frames between girders. The adjustable cross-frame assembly includes a first elongate rigid beam, a second elongate rigid beam, and an adjustable-length jack assembly. The first elongate rigid beam is coupled to a first portion of a first girder and to a first portion of a second girder. The first elongate rigid beam extends in a direction approximately parallel with a plane intersecting both of the first and second girders. The second elongate rigid beam is coupled to a second portion of the first girder and to a second portion of the second girder. The second elongate rigid beam extends in a direction approximately parallel with the plane. The adjustable-length jack assembly is coupled to the first portion of the first girder and to the second portion of the second girder. The adjustable-length jack assembly extends in a direction approximately parallel with the plane.

In another aspect, embodiments disclosed herein relate to a method of installing cross-frames between girders. The method includes coupling a first elongate member of a fixed length to a first portion of a first girder and to a first portion of a second girder. The first elongate member extends in a direction approximately parallel with a first plane intersecting both of the first and second girders. The method further includes coupling a second elongate member of a fixed length to a second portion of the first girder and to a second portion of the second girder. The second elongate member also extends in a direction approximately parallel with the first plane. The method also includes coupling an adjustable-length jack assembly to the first portion of the first girder and to the second portion of the second girder. The adjustable-length jack assembly also extends in a direction approximately parallel with the plane. The adjustable-length jack assembly includes a variable-length strut (e.g., a pipe strut) and a jack (e.g., a double-acting hydraulic jack). The method further includes adjusting a length of the adjustable-length jack assembly by actuating the jack, thereby rotating at least one of the first and second girders to make the first and second girders locally approximately parallel with each other. The method also includes installing a cross-frame coupling the first and second girders together. The method further includes removing the first elongate member, the second elongate member, and the adjustable-length jack assembly from the first and second girders.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1(A) illustrates the drop of adjacent girders and the installed cross-frame.

FIG. 1(B) illustrates a cross-frame installed on a single girder.

FIG. 1(C) illustrates the installation of a cross-frame to an adjacent girder.

FIG. 1(D) illustrates the differential vertical deflection showing misalignment of bolt holes for cross-frame installation.

FIG. 2(A) illustrates the installation of a cross-frame when no force-fitting would be required as the geometry of the girders is at the target geometry, as defined by the target diagonal lengths L1 _(T) and L2 _(T).

FIGS. 2(B)-2(D) illustrate a process of utilizing an adjustable cross-frame assembly for the fit-up of two girders in the case of a skewed bridge with differential vertical deflection.

FIGS. 3(A)-3(C) illustrate a process of utilizing an adjustable cross-frame assembly for the fit-up of two girders in the case of a curved bridge with differential vertical deflection and rotation.

FIG. 4(A) illustrates a plan for a highly skewed prototype bridge.

FIG. 4(B) illustrates a cross-section of the girders and cross-frame of the bridge of FIG. 4(A).

FIG. 4(C) illustrates a portion of the plan of FIG. 4(A) with crane positioning for construction of the bridge.

FIG. 5(A) illustrates a plan for a curved prototype bridge.

FIG. 5(B) illustrates a cross-section of the girders and cross-frame of the bridge of FIG. 5(A).

FIG. 5(C) illustrates a portion of the plan of FIG. 5(A) with crane positioning for construction of the bridge.

FIGS. 6(A) and 6(B) illustrate perspective views of cross-frame installation of a skewed bridge and a curved bridge, respectively.

FIG. 7(A) illustrates a three-dimensional finite-element model of a highly skewed bridge prototype structure prior to installation of any cross-frames.

FIG. 7(B) illustrates a three-dimensional finite-element model of a curved bridge prototype structure prior to installation of any cross-frames.

FIG. 8 illustrates the behavior of a skewed bridge under steel dead load.

FIGS. 9(A) and 9(B) illustrate the behavior of a curved bridge under steel dead load.

FIG. 10 illustrates a skewed bridge deployment plan for the adjustable cross-frame assembly and cross-frames.

FIG. 11 illustrates the skewed bridge of FIG. 10 during step 5 of the deployment sequence.

FIG. 12 illustrates a fit-up comparison for the skewed bridge, when using the adjustable cross-frame assembly as compared to when it is not used.

FIG. 13(A) illustrates a detailed schematic of an embodiment of the adjustable cross-frame assembly including standard bolt connections and chain falls including the elongate flexible lines.

FIG. 13(B) illustrates a detailed schematic of an embodiment of the adjustable cross-frame assembly including clamp brackets and elongate rigid beams.

DETAILED DESCRIPTION

One or more embodiments are described and illustrated in the following description and accompanying drawings. These embodiments are not limited to the specific details provided herein and may be modified in various ways. Furthermore, other embodiments may exist that are not described herein.

In addition, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. For example, the use of “including,” “containing,” “comprising,” “having,” and variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. The terms “connected” and “coupled” are used broadly and encompass both direct and indirect connecting and coupling. Further, “connected” and “coupled” are not restricted to physical or mechanical connections or couplings and can include electrical connections or couplings, whether direct or indirect. In addition, electronic communications and notifications may be performed using wired connections, wireless connections, or a combination thereof and may be transmitted directly or through one or more intermediary devices over various types of networks, communication channels, and connections. Moreover, relational terms such as first and second, top and bottom, and the like may be used herein solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions.

The design, fabrication, and installation of cross-frames for curved and highly skewed steel girder bridges can be difficult and time-consuming. In these bridges, the girders twist and deflect such that there is only one fit condition for which girders are plumb and cross-frames could be installed without force-fitting. This interaction between interim girder geometry and cross-frame fit can result in the following challenges: (1) un-planned force-fitting and hole reaming may be required in the field, (2) girder webs do not meet plumbness requirements, potentially resulting in high locked-in stresses, both in the cross-frames and girders, (3) excessive bearing rotations, and (4) poor joint alignment.

Three fit conditions that are typically used in practice, with the assumption that the girder webs are plumb and the cross-frames are minimally loaded in only one of these configurations, are: (1) No Load Fit (NLF), (2) Steel Dead Load Fit (SDLF), or (3) Total Dead Load Fit (TDLF). Since the designer or owner chooses one condition for the fabricator/erector, this implies that both girders and cross-frames are designed for the interim conditions and that any locked-in forces in the final composite condition do not compromise the overall load-carrying ability of the system.

In a skewed girder bridge, each consecutive girder with identical span length stiffness and cross-section has a different deflection along a line perpendicular to the structure. If the cross-frames are detailed for TDLF but are installed under only the deflection of the steel dead load, the installer will be required to apply additional external forces to the girder and cross-frame system to force-fit the connections, causing some temporary torsional and vertical distortion in each of the girders. In a curved girder system, the effects are exaggerated since the girder center of gravity falls outside the line of action between the supports. Steel girders in this system, whether skewed or normal, have both vertical bending and torsion that amplifies the relative displacements between girders and dramatically complicates fit-up.

The more curved and skewed a bridge is, there is a strong tendency toward SDLF, given that this enhances constructability in the field. However even this can present challenges, as there are often circumstances where curved girders are picked in pairs with cross-frames already installed (i.e., in the NLF condition) or the use of intermediate props or hold cranes introduces another unforeseen set of assumptions. Any changes impact cross-frame forces, camber, and therefore final girder forces, leaving the potential for new bridges to have overstressed components.

As an example, for SDLF or TDLF, the detailer would typically determine the girder geometry by taking the fully-cambered no load girder geometry and subtract the deflections under the steel dead load or total dead load, respectively. The fully-cambered no load girder geometry would have been determined based on the profile of the road and the total dead load deflections. This calculation would determine the “drop” as shown in FIG. 1(A). Cross-frames CF would typically be detailed to be identical to save in fabrication costs and would be pre-assembled as a rigid, welded unit that would be flown in for attachment to the girders. The cross-frames would typically be attached to one girder first (as shown in FIG. 1(B)) and then attached to the adjacent girder (as shown in FIG. 1(C)). If SDLF was used and the girders are supported as expected in the above calculations to determine the drop, then the cross-frames could be installed easily with no force-fitting. However, if TDLF was used or if SDLF was used but the girders were supported or loaded differently than how the drop was calculated (e.g., temporarily supported using cranes, partially erected before splices were made), then there would be challenges in installing the cross-frames. FIG. 1(D) shows the case of a skewed girder bridge for which the cross-frame was initially bolted onto Girder G1 and a bolt hole mis-alignment results in Girder G2 due to a differential vertical deflection. In the case of a curved girder bridge, the girders would also rotate relative to one another, further complicating the cross-frame installation.

In current practice, the designer typically assumes an erection strategy, requiring that the fabricator use the same assumptions and to lock into a specific geometry. Just as importantly, shop fabrication tolerances and restrictions associated with progressive laydown of curved and skewed girder bridges can influence fit-up. The erector then has the challenge of building the bridge as fabricated which likely differs from his/her means and methods. This makes erection more complicated and requires some degree of force-fitting. Force-fitting induces forces that the designer did not anticipate, potentially invalidating the design. This can lead to restrictions on erection, which adds cost and complexity to the project and often involves re-evaluation by the designer. The fabricator spends a lot of time with precision fabrication, and all of this effort at achieving geometry ends up making erection more difficult instead of easier.

Current practice for cross-frame installation when alignment is not achieved involves conventional steel erection equipment such as drift pins, “come-along” tools, chain winches, timber blocking, and crane load manipulation. Such methods are not precise and often involve no definite plan other than installing all required bolts. For example, if the top of the two girder field segments being erected are 2.67 m (8 feet and 9 inches) apart and should be 2.59 m (8 feet and 6 inches) apart, come-along tools might be attached to the opposing top flanges and used to pull the tops together. Likewise, timber blocking might be used between bottom flanges to maintain a particular spacing. In order to install the bolts in the prefabricated cross-frame, drift pins, additional hand-pulling, and crane load manipulation may all need to be employed. These techniques are performed in an ad-hoc manner and may induce unknown stresses in the cross-frames and/or girders, as well as pose safety hazards to the workers conducting the tasks.

It would be desirable to provide a cost-effective, deployable tool for the construction of highly skewed and curved steel girder bridges. Such a device and method could provide the necessary geometry adjustments to the adjacent girders for the fit-up and installation of cross-frames.

To address these challenges in installing cross-frames, an adjustable cross-frame assembly 100 can provide geometry adjustments in adjacent girders G1, G2 for fit-up and installation of cross-frames CF without force-fitting. FIG. 2(A) illustrates the installation of a cross-frame when no force-fitting would be required as the geometry of the girders is at the target geometry, as defined by the target diagonal lengths L1 _(T) and L2 _(T). FIG. 2(B) shows an exaggerated view of two girders G1, G2 of a highly skewed bridge with a differential vertical deflection, with these deflections caused by the steel dead load. FIG. 3(A) shows an exaggerated view of two girders G1, G2 of a curved bridge for which there is both a differential vertical deflection and a rotation, with these deflections and rotations caused by the steel dead load. These differential deflections and/or rotations illustrate the challenge of inserting rigid cross-frames between adjacent girders. The dimensions L₁ and L2 indicate the length of the diagonals between girders, which do not match the target geometry (defined by the target diagonal lengths L1 _(T) and L2 _(T)) for cross-frame installation (as illustrated in FIG. 2(A)).

Turning now to FIG. 2(C) in the case of a highly skewed bridge with a differential vertical deflection or to FIG. 3(B) in the case of a curved bridge for which there is both a differential vertical deflection and a rotation, the adjustable cross-frame assembly 100 includes two elongate flexible lines 102, 104 (which may remain nearly constant in length) and an adjustable-length jack assembly 106. The adjustable cross-frame assembly 100 can be installed near the location where a cross-frame CF should be installed [e.g., approximately 152 mm (6 inches) longitudinally from the location of the cross-frame CF installation] or at other locations along the length of the bridge [e.g., midway between where two cross-frames CF would be installed]. Specifically, the first elongate flexible line 102 is coupled in tension to an upper portion of the first girder G1 and to an upper portion of the second girder G2. The first elongate flexible line 102 extends along a plane intersecting both of the girders G1, G2 [the plane being the page showing the cross-section in either of FIG. 2(C) or 3(B)]. The second elongate flexible line 104 is coupled in tension to a lower portion of the first girder G1 and to a lower portion of the second girder G2. The second elongate flexible line 104 extends along the same plane as the first elongate flexible line 102. In some embodiments, the first and second elongate flexible lines 102, 104 are allowed to go slack during the installation process. The adjustable-length jack assembly 106 is coupled to the upper portion of the first girder G1 and to the lower portion of the second girder G2. The adjustable-length jack assembly 106 also extends along the same plane as the elongate flexible lines 102, 104.

As shown in FIG. 2(D) in the case of a highly skewed bridge with a differential vertical deflection or in FIG. 3(C) in the case of a curved bridge for which there is both a differential vertical deflection and a rotation, the adjustable-length jack assembly 106 can then be lengthened or shortened to rotate the girders G1, G2 to a small angle α such that the girders are approximately parallel to one another. This adjustment allows the cross-frame CF to be installed without force-fitting. This rotation changes the dimensions of the diagonals to become approximately the target lengths of L1 _(T) and L2 _(T). In some embodiments, the dimensions of the diagonals are within ⅛ of an inch of the target lengths of L1 _(T) and L2 _(T).

The permanent cross-frame CF is then installed and the adjustable cross-frame assembly 100 is then removed. The adjustable cross-frame assembly 100 is then available to be used once more at another location along the girders G1, G2 and/or for other girder lines along the same structure or on other structures.

The geometry adjustment may be considered adequate (e.g., minimal to no force-fitting is required for the installation of a permanent, rigid cross-frame CF) if the diagonal lengths L1 and L2 match their respective target (ideal) lengths (L1 _(T) and L2 _(T)) within a threshold of, for instance, 3.18 mm (⅛ inches) [such that |δL|<3.18 mm (⅛ inches), where δL=L_(γ)−L, for L1 and L2].

The adjustable cross-frame assembly 100 increases flexibility in fabrication and erection while reducing the potential for overstress in the system. The use of the adjustable cross-frame assembly 100 may enable fabrication using one set of fit assumptions and field adjustments to accommodate another set of assumptions, whether that be from different erection assumptions, fabrication tolerances, camber variations, or other unanticipated geometry variations.

To demonstrate the adjustable cross-frame assembly 100 in a realistic construction scenario, the behaviors of a highly skewed steel girder bridge and a curved steel girder bridge that have recently been constructed have been investigated.

As shown in FIG. 4(A), the highly skewed prototype bridge is a simply supported, 71.0-m (233-ft) long bridge. The bridge includes first and second girders G1, G2. The bridge includes two sections of girders, with adjacent girders of each section spaced apart by 2.57 m (or 8 feet 5 inches) for a total width W of each section being 18 m (or 58 feet 11 inches). The two sections of girders are separated by a space S of 1.35 m (or 4 feet 5 inches). Each girder has a length L of 71 m (or 233 feet). The girders are also skewed by an angle A of 30°.

FIG. 4(B) shows the cross-section of the girders G1, G2 with an intended cross-frame CF installed. The research focused on the behavior of the girders G1, G2 under steel dead load at the construction increment when the cross-frames CF are to be installed. In this embodiment, the top flange of each girder G1, G2 in FIG. 4(B) includes ends having measurements of 38.1 mm by 610 mm (1½ inches by 24 inches) and a middle having measurements of 41.3 mm by 762 mm (1⅝ inches by 30 inches). The web of each girder G1, G2 includes ends having measurements of 20.6 mm by 2.34 m ( 13/16 inches by 92 inches) and a middle having measurements of 19.1 mm by 2.34 m (¾ inches by 92 inches). The bottom flange of each girder G1, G2 includes ends having measurements of 38.1 mm by 813 mm (1½ inches by 32 inches) and a middle having measurements of 54 mm by 813 mm (2⅛ inches by 32 inches). A top horizontal member T (e.g., formed of two L-shaped members back-to-back) of the cross-frame CF is 6 inches by 6 inches by ⅞ inches. The two cross members D1, D2 (e.g., each cross member formed of L-shaped members) are each 8 inches by 8 inches by ¾ inches. The bottom horizontal member B (e.g., formed of two L-shaped members back-to-back) is 6 inches by 6 inches by ⅞ inches. The gusset plates P1, P3 are each 19.1 mm (¾ inches) thick. The stiffener plate P2 is 12.7 mm (½ inches) thick.

As shown in FIG. 4(C), at this construction increment, the first girder G1 has been erected and spans between two abutments while also being supported by two cranes C3, C4. Temporary braces are also used to provide lateral stability at the top of the cross-section at each abutment for the first girder G1. Part of the second girder G2 (up to the field splice location) is supported by one abutment and two cranes C1, C2. Based on the erection engineering documentation, the crane forces at this increment are: crane C1—165 kN (37 kips); crane C2—236 kN (53 kips); crane C3—369 kN (83 kips); and crane C4—111 kN (25 kips). No cross-frames have been installed at this construction increment. The distance D1 between the far-left abutment and crane C1 is 10.9 m (35 feet 9 inches). The distance D2 between crane C1 and crane C2 is 32.6 m (106 feet 11 inches). The distance D3 between the far-left abutment and crane C3 is 47.1 m (154 feet 7 inches). The distance D4 between the far-left abutment and crane C4 is 6.27 m (20 feet 7 inches). The distance D5 between crane C2 and the splice location of the second girder G2 is 5.69 m (18 feet 8⅛ inches).

As shown in FIG. 5(A), the curved prototype bridge is one span of a curved ramp, with a length L of 60.4 m (198 feet) and an inner radius of 295 m (968 feet). The bridge includes first and second girders G1, G2. The bridge includes one section of girders, with adjacent girders spaced apart by 2.44 m (8 feet) for a total width W of 12.2 m (40 feet).

FIG. 5(B) shows the cross-section of the girders G1, G2 with an intended cross-frame CF installed. The research focused on the behavior of the girders G1, G2 under steel dead load at the construction increment when cross-frames CF are installed. In this embodiment, the top flange of each girder G1, G2 in FIG. 4(B) is 41.3 mm by 508 mm (1⅝ inches by 20 inches). The web of each girder G1, G2 is 17.5 mm by 2.51 m ( 11/16 inches by 99 inches). The bottom flange of each girder G1, G2 is 38.1 mm by 559 mm (1½ inches by 22 inches). The top member T (e.g., formed of a C-shaped member) is 229 mm by 318 mm (9 inches by 15 inches). The two cross members D1, D2 (e.g., each cross member formed of L-shaped members) are each 127 mm by 127 mm by 12.7 mm (5 inches by 5 inches by ½ inches). The bottom member B (e.g., formed of a C-shaped member) is 229 mm by 318 mm (9 inches by 15 inches). The gusset plates P1, P3 are each 14.3 mm ( 9/16 inches) thick. The stiffener plate P2 is also 14.3 mm ( 9/16 inches) thick.

Both girders G1, G2 are supported at one pier and segments extend past the field splice and onto temporary falsework (not shown). At the pier, the top of the cross-section of the first girder G1 is laterally braced with a temporary support. The first girder G1 is also supported by crane C3, and the second girder G2 is supported by cranes C1, C2. Based on the erection engineering documentation, the crane forces at this increment are: crane C1—142 kN (32 kips); crane C2—4.45 kN (1 kip); and crane C3—142 kN (32 kips). No cross-frames have been installed at this construction increment. The distance D1 between the pier and crane C1 is 10.7 m (31 ft). The distance D2 between crane C1 and crane C2 is 42.1 m (138 ft). The distance D3 between the pier and crane C3 is 22.9 m (75 ft). The distance D4 between crane C3 and the end of the first girder G1 is 24.4 m (80 ft).

FIGS. 6(A) and 6(B) show the cross-frame installation for each prototype bridge using conventional methods of erection.

Three-dimensional finite element (FE) analyses of the prototype bridges were performed to understand the differential vertical deflection and/or rotation at the construction increment before cross-frame CF installation. The efficacy of the adjustable cross-frame assembly 100 is then demonstrated for the highly skewed bridge.

For both types of analyses, the FE models were built in the software package ABAQUS (2022), using S4R or S3R general-purpose shell elements. Static analyses of the increment of construction when cross-frames CF would be installed were performed under the steel dead load. Nonlinear geometry was assumed. A linear material model for the steel girders and cross-frames was assumed, with a Young's modulus of 200 GPa (29,000 ksi) and density of 7,850 kg/m³ (0.490 kcf). A mesh size of 152 mm (6 inches) was used based on the results from mesh refinement studies.

FIGS. 7(A) and 7(B) show the FE models for each of the prototype bridges, including the boundary conditions. Boundary conditions can be the resulting condition of any appropriate structure (natural or humanmade) restraining translation and/or rotation of, for instance, the girders. Boundary conditions that restrain translation in a direction are indicated by arrows. More specifically, at the abutment for the highly skewed bridge and the pier for the curved bridge, a single node at the intersection of the bottom flange to the web is restrained in the transverse (z-direction) and vertical (y-direction), simulating elastomeric bearings. For the highly skewed bridge, additional longitudinal restraint from the bearings is modeled as springs with a stiffness of 6.13 kN/mm (35 kips/in). Also, for the highly skewed bridge, a single node at the intersection of the top flange to the web is restrained in the transverse direction to simulate temporary erection braces at each end of the first girder G1. For the curved girder bridge, this restraint representing a temporary erection brace is applied only at the abutment of the first girder G1. The cranes were modeled as truss elements with a Young's modulus of 103 GPa (15,000 ksi) and a cross-sectional area of 1,770 mm² (2.75 in²) to represent realistic crane ropes. Displacements were prescribed at the top of the crane truss element to match the displacement of the girders at crane support locations in the model with those in the available construction engineering documents. For the curved bridge, FIG. 5(C) shows only a partial view of the construction stage, from the pier to the splices. In fact, the girders G1, G2 extend to temporary falsework. The effect of this additional restraint is modeled numerically through prescribed displacements.

For the highly skewed bridge shown in FIG. 7(A), the geometry of the web was modeled based on the fully-cambered no load girder geometry, taken from the web blocking diagram of the fabrication drawings for the bridge. As differential vertical deflections are the predominant challenge in cross-frame installation of straight, skewed bridges, it was important to capture this geometry. The flanges follow the geometry of the web.

For the curved bridge shown in FIG. 7(B), the geometry of the web was assumed to be flat, as there was little difference in camber between the two girder lines in the design and avoiding doubly-curved surfaces reduced the model complexity.

For both bridges, no transverse slope was modeled (i.e., both girder lines were assumed to be at the same vertical position), for simplicity. For the highly skewed bridge shown in FIG. 7(A), an additional 8.90 kN (2 k) load is applied at the splice location on both girder lines to represent the weight of the splices.

No cross-frames were modeled when investigating the behavior under steel dead load.

When investigating behavior using the adjustable cross-frame assembly 100, a staged FE model was developed to understand behavior at each step of the deployment sequence of the adjustable cross-frame assembly 100. In the first stage of the FE model, both girders G1, G2, all cross-frames, and the adjustable cross-frame (at each location where it will be used) are in the assembly. Then the boundary conditions are applied and all cross-frames are de-activated (such that not even the effect of their dead load is incorporated in the model). The dead load is applied to all active components. This corresponds to Step 1 of the sequence to be discussed later. Then, in individual stages and according to the desired sequence, the adjustable cross-frame assembly 100 is utilized or cross-frames CF are activated.

For modeling of the adjustable cross-frame assembly 100, the elongate flexible lines 102 were modeled as tension-only truss elements with a Young's modulus of 103 GPa (15,000 ksi) and a cross-sectional area of 269 mm² (0.417 in²). The adjustable-length jack assembly 106 was modeled as a truss element with a Young's modulus of 200 GPa (29,000 ksi) and a cross-sectional area of 2,030 mm² (3.14 in²), allowing both tension and compression. “Coupling” constraints were used to represent “pin” connections (i.e., translation is coupled in all directions, but rotation is not), joining the adjustable cross-frame assembly 100 to the girders G1, G2. At a stage when the adjustable cross-frame assembly 100 is not in use, the Young's modulus is reduced to a negligibly small value such that it has an insignificant impact on behavior. At a stage when the adjustable cross-frame assembly 100 is in use, the Young's modulus is increased to the desired 103 GPa (15,000 ksi) value and a thermal load is applied to the truss element that represents the adjustable-length jack assembly 106, thereby simulating the elongation and/or contraction of the jack. The magnitude of the thermal load (which relates to the magnitude of the increase or decrease in length of the adjustable-length jack assembly 106) was determined based on the difference between the current length of the diagonals, L1 and L2 at the cross-frame location at the prior step as compared to the target length of the diagonals L1 _(T), L2 _(T) at the cross-frame location.

At a stage where a cross-frame CF would be installed, that part is then activated. The cross-frames CF are modeled as shell elements with the form and section sizes as shown in FIG. 4(B) for the highly skewed bridge and FIG. 5(B) for the curved bridge.

FIG. 8 shows the differential vertical deflection between the girders G1, G2 for the highly skewed prototype bridge (FIG. 7(A)). For the highly skewed prototype bridge, the differential vertical deflection, D at a given cross-frame location (indicated by dashed vertical lines) is calculated as followings:

D=(y _(DL−G1) −y _(DL−G2))−d

where y_(DL−G1) is the vertical coordinate of girder G1 under steel dead load only when it is supported per the construction increment shown in FIG. 4(C), y_(DL−G2) is the vertical coordinate of girder G2 under steel dead load only when supported per the construction increment shown in FIG. 4(C), and d is the drop (see FIG. 1(A)). In this investigation, the drop, d is calculated for each girder G1, G2 by subtracting the deflections under the steel dead load that were calculated by the designer assuming a certain set of boundary conditions from the fully-cambered no load girder geometry (which corresponds to the web blocking diagram from the fabrication documents). In this investigation, it is assumed that SDLF was chosen as the fit condition. The differential vertical deflection, D results because the designer assumed a different set of boundary conditions when calculating the deformed shape of the girders under steel dead load than the actual boundary conditions when the cross-frames are installed at the construction increment shown in FIG. 4(C) (e.g., in this case, the girders are supported by cranes, temporary braces are used, and girder G2 is not erected at its full length). In reality, this structure was detailed for TDLF but the cross-frames are installed under steel dead load. Similar types of differential vertical deflections would result, but are not studied in this document.

The peak differential vertical deflection occurs at cross-frame location 3 with a magnitude of 11.4 mm (0.448 in). In comparison, the differential vertical deflections at location 8 and 9 are less than 3.18 mm (0.125 in.), such that these two cross-frames could be installed with limited to no force fitting. Along the entire girder length, there is negligible rotation, as expected for a straight, skewed bridge.

FIG. 9(A) shows the differential vertical deflection, D between the girders G1, G2 for the curved prototype bridge (FIG. 5(B)) when it is supported per the construction increment shown in FIG. 5(C). As the model for the curved bridge did not include camber, the drop, d is zero. Therefore, this data reflects only the relative deflection of each girder under dead load. The peak differential vertical deflection is at cross-frame location 4 with a magnitude of 7.26 mm (0.286 in). With reference to FIG. 9(B), as expected for a curved girder bridge, each girder rotates under the steel dead load, with the second girder G2 featuring the peak rotation at 1.07 degrees at cross-frame location 3.

These differential vertical deflections and rotations are unique to the prototype bridges investigated here, the fit conditions assumed in this investigation, and the modeling assumptions made in this investigation

Given the differential vertical deflections/and or girder rotations found for the prototype bridges, a control sequence of when and where the deployable tool should be used, including the installation of the cross-frames, was developed. The forces in the deployable tool during adjustment and the stresses in the installed cross-frames were evaluated during this process.

TABLE 1 Highly Skewed Prototype Bridge: Control Sequence and Forces in Adjustable Cross-Frame Assembly Forces in Adjustable Cross-Frame Assembly [kN (kips)] Adjustable- First Second Length Jack Elongate Elongate Step Task Location Assembly Flexible Line Flexible Line 1 Initial — — — 2 Install Cross-frame 8, 9 — — — 3 Install adjustable 1 −16.0 0.326 7.42 cross-frame assembly (−3.61) (0.0733) (1.67) 4 Install Cross-frame 1 −16.0 0.0259 7.53 (−3.60) (0.0582) (1.69) 5 Remove adjustable 1 — — — cross-frame assembly 6 Install Cross-frame 7 7 Install adjustable 3 −2.17 3.94 1.32 cross-frame assembly (−0.487) (0.886) (0.298) 8 Install Cross-frame 3 −2.08 3.90 1.41 (−0.467) (0.876) (0.317) 9 Remove adjustable 3 — — — cross-frame assembly 10 Install Cross-frame 2, 4 — — —

In this investigation, the philosophy for determining the sequence was developed with the aim of (1) simplifying the necessary analyses to be performed by the engineer to use adjustable cross-frame assembly 100 and (2) minimizing the number of times the adjustable cross-frame assembly 100 would need to be used to install the cross-frames as rapidly as possible.

A philosophy for determining the sequence, which is used in this investigation, is as follows. An engineer performs an analysis of the construction stage when cross-frames would be installed to determine the differential vertical deflections/rotations under steel dead load (with no cross-frames included in the analysis). With the assumption that cross-frames could be installed with minimal or no force-fitting if the differential vertical deflection, D is less than 3.18 mm (0.125 in.) and/or |δL|<3.18 mm (⅛ in) for both diagonals L1, L2, it would be recommended that any cross-frame locations for which the differential vertical deflection, D is less than 3.18 mm (0.125 in.) and/or |δL|<3.18 mm (⅛ in) for both diagonals L1, L2 be installed first. Then the adjustable cross-frame assembly 100 would be deployed near the cross-frame location with the highest differential vertical deflections/rotations. The jack assembly 106 would either extend or contract, as necessary such that |δL|<3.18 mm (⅛ in) for both diagonals L1, L2. That cross-frame would then be installed. The adjustable cross-frame assembly 100 would then be removed and reused elsewhere. Note that while the adjustable cross-frame assembly 100 is deployed, the contractor could inspect for any other cross-frames that could be installed without force fitting and install those as well. This could be done while the adjustable cross-frame assembly 100 is deployed or after it is removed.

The contractor would then determine where the adjustable cross-frame assembly 100 should be deployed next based on observing which cross-frame would be the next most difficult to install. This could also be determined based on the largest difference SL between the diagonal lengths L1, L2 and the target lengths L1 _(T), L2 _(T) at each cross-frame location. This would be repeated as needed until all cross-frames are installed. As un-anticipated geometry variations may occur, the contractor could alter this sequence as needed. The engineer could specify a maximum allowable force that could be used in the adjustable-length jack assembly 106 and allow the contractor to use any amount of force necessary up to this maximum allowable force at each time the contractor uses the adjustable cross-frame assembly 100.

If the differential vertical deflections are greater than 3.18 mm (0.125 in.) and/or |δL|>3.18 mm (⅛ in) for either diagonal L1 or L2 at the cross-frame nearest to a support or boundary condition, then the adjustable cross-frame assembly 100 could be used to facilitate the installation of that cross-frame first (even if it isn't the one with the highest differential vertical deflections and/or rotations). This is to overcome the challenge of installing cross-frames near support or boundary conditions which resist relative geometry changes of the girders. After this, then the cross-frames with the highest differential vertical deflections/rotations should be installed.

Throughout this procedure the threshold of |δL|<3.18 mm (⅛ in) for both diagonals L1, L2 has been used to indicate that a cross-frame can be installed with no or minimal force fitting. Other thresholds could be specified.

Alternatively, one can envision that the contractor can use the adjustable cross-frame assembly 100 where it is needed based on the contractor's observations or experience. An engineer could prescribe a maximum allowable force that could be used in the adjustable-length jack assembly 106 and allow the contractor to use any amount of force necessary up to this maximum allowable force. This approach would permit more flexibility for overcoming different erection assumptions, fabrication tolerances, camber variations, or other unanticipated geometry variations. Other sequences could also be envisioned, for example based on site conditions and which locations may be the easiest for the adjustable cross-frame assembly 100 to be deployed.

In this investigation, the adjustable cross-frame assembly 100 is installed 6 in. away from the cross-frame location with the highest magnitude of differential vertical deflections/rotations. Alternatively, it could be placed midway between two cross-frame locations with the highest magnitudes of differential vertical deflections/rotations, with the aim of facilitating the installation of two cross-frames at once.

At each time the adjustable cross-frame assembly is installed, the user should evaluate if the jack assembly 106 should be extended or contracted, based on the current diagonal lengths L1, L2 as compared to the target diagonal lengths L1 _(T), L2 _(T). If δL>0, then that diagonal should be lengthened. If δL<0, then that diagonal should be shortened. The users should also determine which orientation the jack assembly 106 should be used in, for example parallel to L1 or parallel to L2.

Table 1 above shows the control sequence for deploying the adjustable cross-frame assembly 100 and installing the cross-frames CF for the highly skewed bridge (FIG. 7(A)), with the locations indicated in FIG. 10 , that is used in this investigation.

Only one adjustable cross-frame assembly 100 is used in the sequence, but it is moved to different locations at different points in the sequence. Alternatively, a contractor could use more than one adjustable cross-frame assembly 100 to achieve the installation of the cross-frames.

Recalling the differential vertical deflections shown in FIG. 8 , cross-frame locations 8 and 9 have differential vertical deflections, D less than 3.18 mm (0.125 in.), meaning that cross-frames CF8, CF9 could be installed with no or minimal force-fitting. As a result, the cross-frames CF8, CF9 are installed at cross-frame location 8 and 9, respectively first, using the sections shown in FIG. 4(B). The form of the cross-frame CF is assumed to be rectangular, with horizontal member T, horizontal member B, and equal length cross members D1, D2. It is installed 102 mm (4 in.) below the top flange of girder G1 and connects to girder G2 at the appropriate vertical location based on its rigid geometry.

As cross-frame location 1 has differential vertical deflections exceeding 3.18 mm (0.125 in.) and it is near the support, the adjustable cross-frame assembly 100 is used to first install this cross-frame CF1, even though the largest different vertical deflection occurs at CF 3. The adjustable cross-frame assembly 100 is installed 152 mm (6 in) away from cross-frame location 1, which is where the next cross-frame CF1 would be installed, in the longitudinal direction. The adjustable-length jack assembly 106 is extended until |δL|<3.18 mm (⅛ in) for both diagonals L1, L2, with forces in the adjustable cross-frame assembly 100 shown in Table 1 above. Note that throughout the present disclosure, positive indicates tension, and negative indicates compression. A cross-frame CF1 is then installed at cross-frame location 1, and the adjustable cross-frame assembly 100 is released. This release results in stresses being imparted into the cross-frame CF1 (with reference to FIG. 11 , Table 2 below).

TABLE 2 Highly Skewed Prototype Bridge: Peak Von Mises Stresses in Cross-Frames CF1 and CF7 Cross-Frame CF1 Stresses Cross-Frame CF7 Stresses [MPa (ksi)] [MPa (ksi)] Step D1 D2 T B D1 D2 T B  4 5.78 4.98 3.38 3.03 — — — — (0.838) (0.722) (0.490) (0.440)  5 8.53 9.28 8.82 4.33 — — — — (1.24) (1.35) (1.28) (0.629)  6 8.75 8.91 8.79 4.55 5.37 5.96 3.10 4.03 (1.27) (1.29) (1.28) (0.660) (0.779) (0.864) (0.450) (0.584)  7 8.83 10.8 22.3 8.29 4.83 6.57 2.89 6.69 (1.28) (1.57) (3.24) (1.20) (0.701) (0.952) (0.420) (0.971)  8 8.88 10.6 22.3 8.42 4.88 6.44 2.86 7.02 (1.29) (1.54) (3.24) (1.22) (0.708) (0.934) (0.415) (1.02)  9 8.89 10.6 22.4 8.43 4.89 6.42 2.86 6.99 (1.29) (1.54) (3.25) (1.22) (0.709) (0.931) (0.415) (1.01) 10 8.85 10.1 22.1 8.54 4.96 6.25 2.96 7.56 (1.28) (1.47) (3.21) (1.24) (0.720) (0.907) (0.429) (1.10) D1 = Diagonal 1; D2 = Diagonal 2; T = Top; B = Bottom of Cross-Frame (FIG. 1(A))

TABLE 3 Highly Skewed Prototype Bridge: Peak Von Mises Stresses in Cross-Frames CF3, CF2, and CF4 Cross-Frame CF3 Stresses Cross-Frame CF2 Stresses Cross-Frame CF4 Stresses [MPa (ksi)] [MPa (ksi)] [MPa (ksi)] Step D1 D2 T B D1 D2 T B D1 D2 T B — — — — — — — — — — — —  5 — — — — — — — — — — — —  6 — — — — — — — — — — — —  7 — — — — — — — — — — — —  8 5.58 (0.955) 3.34 3.40 — — — — — — — — (0.809) 6.58 (0.485) (0.493) — — — — — — — —  9 6.24 6.59 3.65 3.99 — — — — — — — — (0.905) (0.955) (0.529) (0.579) — — — — — — — — 10 6.15 6.59 3.89 4.05 6.33 5.49 15.3 3.90 5.42 6.92 3.43 3.39 (0.892) (0.956) (0.565) (0.588) (0.918) (0.796) (2.214) (0.566) (0.786) (1.00) (0.498) (0.491) D1 = Diagonal 1; D2 = Diagonal 2; T = Top; B = Bottom of Cross-Frame (FIG. 1(A))

After installing cross-frame CF1, it was observed numerically (and could be observed physically by the contractor), that cross-frame CF7 meets the |δL|<3.18 mm (⅛ in) for both diagonals L1, L2. Cross-frame CF7 is then installed. Note that cross-frame CF7 actually met this criterion at Step 1 and could have been installed in Step 2. However, this was not done in this document because the initial decisions on which cross-frame to install at Step 2 were made based solely on the differential vertical deflection, D. Then, the adjustable cross-frame assembly 100 would be used to install the cross-frame that has the highest differential vertical deflection/rotation. In this case, that would be cross-frame CF3 at the cross-frame location 1. The adjustable cross-frame assembly 100 would again be installed 152 mm (6 in) away longitudinally from the cross-frame location 3. In this case, the jack assembly 106 is retracted (as opposed to extended) based on the current lengths L1, L2 as compared to the target lengths L1 _(T), L2 _(T). Then, cross-frame CF3 would be installed, using a similar procedure, at the cross-frame location 3.

It was then observed numerically (and could be observed physically by the contractor), that cross-frames CF2, CF 4 now meet the |δL|<3.18 mm (⅛ in) for both diagonals L1, L2. Cross-frames CF2, CF4 were then installed. And the procedure could continue until all cross-frames were installed.

In some embodiments, throughout the sequence, the force in the adjustable-length jack assembly 106 never exceeded 16.0 kN (3.61 k) (see Table 1 above), which could be readily achieved with off-the-shelf technologies. Further, the stresses in the permanent cross-frames CF remain low [peak von Mises stress is 22.4 MPa (3.25 ksi); see Table 2 and Table 3 above], indicating that the procedure is not over-stressing components. Additionally, the crane forces remained almost constant throughout, indicating that the process was not inducing additional forces on the cranes C. The peak change in force in a crane C was 6.87% [i.e., 237 kN (53.4 k) in Crane 2 in Step 1 compared to 254 kN (57.1 k) in Step 10].

This strategy focused on differential vertical deflections for determining the sequence as it was for a highly skewed bridge where no significant rotations result. If there are significant rotations, these could also be considered in determining the sequence (e.g., in the case of the curved girder bridge).

FIG. 12 provides a fit-up comparison if the adjustable cross-frame assembly 100 is not used (solid) compared to if it is used (dashed). The vertical axis indicates the difference, δL=L_(T)−L for lengths L1 and L2. As mentioned earlier, a threshold of |δL|<3.18 mm (⅛ in) (dotted lines) was used as an indicator of an acceptable length difference for which force-fitting would not be required. This was readily achieved.

This investigation used one approach for determining the sequence for the use of the adjustable cross-frame assembly 100 and installation of the cross-frames. Other approaches could be developed.

FIGS. 13(A) and 13(B) show two more embodiments of the adjustable cross-frame assembly 100, 200. In the embodiment shown in FIG. 13(A), the adjustable cross-frame assembly 100 includes the elongate flexible lines 102, which may be, for instance, adjustable, off-the-shelf items such as chain falls. Stated another way, some embodiments have a first chain fall 108 including the first elongate flexible line 102 and a second chain fall 110 including the second elongate flexible line 104. As stated above, the elongate flexible lines 102, 104 could be cables, but they could also be chains, belts, ropes, or the like. The chain falls 108, 110 and their respective elongate flexible lines 102, 104 are able to remain constant in length during use but are also adjustable between uses to adapt to different spacings between girders G1, G2. This is the case whether the subsequent uses are on the same bridge or a different bridge.

The embodiment in FIG. 13(A) also includes the chain falls 108, 110 and their respective elongate flexible lines 102, 104 coupled to the girders G1, G2 with a plurality of fasteners, such as bolts, coupled to connection plates 112 and to the girders G1, G2 themselves. Stated another way, fasteners pass through both a portion of the respective girder G1, G2 and the respective connection plate 112, and the chain falls 108, 110 and elongate flexible lines 102, 104 are fastened to the connection plates 112. The connection between the chain falls 108, 110 and the connection plates 112 (similar to the connection between the elongate flexible lines 102, 104 and the connection plates 112) may be in the form of a hook of the chain fall 108, 110 (or of the elongate flexible line 102, 104) that is hooked onto a shackle. The shackle is then coupled to the connection plate 112 via a bolt (or other fastener) extending through the connection plate 112 and the shackle to close the loop of the shackle. In some embodiments, the connection plates 112 are welded to the respective girders G1, G2 instead of bolted or otherwise fastened to the respective girders G1, G2. Such embodiments avoid drilling holes into the girders G1, G2.

Also shown in FIG. 13(A), the adjustable-length jack assembly 106 includes a variable-length strut 114 (e.g., a pipe strut) and a jack 116. The jack 116 may be a hydraulic jack. The jack 116 may be a double-acting jack that allows for the upper portion of the first girder G1 to be pulled together with the lower portion of the second girder G2 or for the girders G1, G2 to be pushed apart, due to the fact that the double-acting jack 116 is actuatable in two directions. Other embodiments may include the jack 116 not be double-acting, in which case a user would have to determine the proper arrangement of the adjustable-length jack assembly 106 based on the orientation of the girders G1, G2 such that the actuation direction of the hydraulic cylinder 116 is in a correct direction of movement for the girders G1, G2 relative to each other. Other embodiments may have the jack 116 be a mechanical jack. The jack 116 may be an off-the-shelf jack or a customized jack. The variable-length strut 114 is able to remain constant in length during use but is also adjustable between uses to adapt to different spacings between girders G1, G2 and/or different heights of girders G1, G2.

The embodiment of the adjustable cross-frame assembly 200 shown in FIG. 13(B) has first and second elongate rigid beams 202, 204 instead of elongate flexible lines. In some embodiments, the elongate rigid beams 202, 204 may include rods (e.g., high-strength steel threaded rods). The elongate rigid beams 202, 204 may be in the same arrangement as the prior-described elongate flexible lines 102, 104, but the elongate rigid beams 202, 204 would be configured to provide compression forces in addition to tension forces on the portions of the girders G1, G2.

Also shown in FIG. 13(B), the cross-frame assembly 200 includes clamp brackets 218 that removably clamp to or at least partially surround the girders G1, G2 instead of requiring holes for fasteners to be drilled in the girders G1, G2 (for the attachment of plates) or plates be welded to the girders G1, G2. This alternative arrangement could likewise be applied to the previously described cross-frame assembly 100.

In some embodiments, the elongate flexible lines 102, 104 are configured to pull while the adjustable-length jack assembly 106 is configured to push. In other embodiments, the elongate rigid beams 202, 204 are configured to push while the adjustable-length jack assembly 106 is configured to pull. In some embodiments, both an elongate flexible line and an elongate rigid beam may be used together, such that the elongate flexible line is configured to pull and the elongate rigid beam is configured to push. In some embodiments, the elongate rigid beams are also capable of pulling.

Other embodiments contemplated herein could include a plurality of adjustable-length jack assemblies 106 in various orientations and locations to accomplish the same or similar tasks.

While the focus of this disclosure has been on the use of the adjustable cross-frame assembly to facilitate cross-frame installation for highly skewed and curved girder bridges, the adjustable cross-frame assembly 100 also has the potential to aid in the addition of girder lines to widen a bridge. A potential additional application includes stabilizing girders during deck replacement. While I-beams have been illustrated and described, the present disclosure contemplates any form of beam. While steel beams have been illustrated and described, the present disclosure contemplates beams of any material (e.g., prestressed concrete).

Various features and advantages of some embodiments are set forth in the following claims. 

What is claimed is:
 1. An adjustable cross-frame assembly for installing cross-frames between girders, the adjustable cross-frame assembly comprising: a first elongate flexible line coupled in tension to a first portion of a first girder and to a first portion of a second girder, the first elongate flexible line extending in a direction approximately parallel with a plane intersecting the first and second girders; a second elongate flexible line coupled in tension to a second portion of the first girder and to a second portion of the second girder, the second elongate flexible line extending in a direction approximately parallel with the plane; and an adjustable-length jack assembly coupled to the first portion of the first girder and to the second portion of the second girder, the adjustable-length jack assembly extending in a direction approximately parallel with the plane.
 2. The adjustable cross-frame assembly of claim 1, further comprising a first chain fall including the first elongate flexible line and a second chain fall including the second elongate flexible line.
 3. The adjustable cross-frame assembly of claim 2, wherein the adjustable-length jack assembly includes a hydraulic jack.
 4. The adjustable cross-frame assembly of claim 3, wherein the hydraulic jack includes a double-acting hydraulic cylinder.
 5. The adjustable cross-frame assembly of claim 4, wherein the adjustable-length jack assembly includes a variable-length pipe strut.
 6. The adjustable cross-frame assembly of claim 1, wherein each of the first elongate flexible line and the second elongate flexible line includes a cable.
 7. The adjustable cross-frame assembly of claim 1, wherein each of the first elongate flexible line, the second elongate flexible line, and the adjustable-length jack assembly is bolted to both of the first and second girders.
 8. The adjustable cross-frame assembly of claim 7, wherein each of the first and second girders includes plates coupled thereto, and each of the first elongate flexible line, the second elongate flexible line, and the adjustable-length jack assembly is coupled to one or more of the plates.
 9. The adjustable cross-frame assembly of claim 1, further comprising a plurality of clamp brackets configured to removably couple each of the first elongate flexible line, the second elongate flexible line, and the adjustable-length jack assembly to the first and second girders.
 10. An adjustable cross-frame assembly for installing cross-frames between girders, the adjustable cross-frame assembly comprising: a first elongate rigid beam coupled to a first portion of a first girder and to a first portion of a second girder, the first elongate rigid beam extending in a direction approximately parallel with a plane intersecting the first and second girders; a second elongate rigid beam coupled to a second portion of the first girder and to a second portion of the second girder, the second elongate rigid beam extending in a direction approximately parallel with the plane; and an adjustable-length jack assembly coupled to the first portion of the first girder and to the second portion of the second girder, the adjustable-length jack assembly extending in a direction approximately parallel with the plane.
 11. The adjustable cross-frame assembly of claim 10, wherein each of the first elongate rigid beam and the second elongate rigid beam includes a threaded rod.
 12. The adjustable cross-frame assembly of claim 11, wherein the adjustable-length jack assembly includes a hydraulic jack.
 13. The adjustable cross-frame assembly of claim 12, wherein the hydraulic jack includes a double-acting hydraulic cylinder.
 14. The adjustable cross-frame assembly of claim 13, wherein the adjustable-length jack assembly includes a variable-length pipe strut.
 15. The adjustable cross-frame assembly of claim 10, further comprising a plurality of clamp brackets configured to removably couple each of the first elongate rigid beam, the second elongate rigid beam, and the adjustable-length jack assembly to the first and second girders.
 16. The adjustable cross-frame assembly of claim 10, wherein each of the first and second girders includes plates coupled thereto, and each of the first elongate rigid beam, the second elongate rigid beam, and the adjustable-length jack assembly is coupled to one or more of the plates.
 17. The adjustable cross-frame assembly of claim 10, wherein the first portion of the first girder includes an upper third of the first girder, the first portion of the second girder includes an upper third of the second girder, the second portion of the first girder includes the lower third of the first girder, and the second portion of the second girder includes the lower third of the second girder.
 18. A method of installing cross-frames between girders, the method comprising: coupling a first elongate member of a fixed length to a first portion of a first girder and to a first portion of a second girder, such that the first elongate member extends in a direction approximately parallel with a first plane intersecting both of the first and second girders; coupling a second elongate member of a fixed length to a second portion of the first girder and to a second portion of the second girder, such that the second elongate member extends in a direction approximately parallel with the first plane; coupling an adjustable-length jack assembly to the first portion of the first girder and to the second portion of the second girder, such that the adjustable-length jack assembly extends in a direction approximately parallel with the first plane, the adjustable-length jack assembly including a variable-length strut and a jack; adjusting a length of the adjustable-length jack assembly by actuating the jack, thereby rotating at least one of the first and second girders to make the first and second girders locally approximately parallel with each other; installing a cross-frame coupling the first and second girders together; and removing the first elongate member, the second elongate member, and the adjustable-length jack assembly from the first and second girders.
 19. The method of claim 18, further comprising coupling the first elongate member to a first portion of the first girder and to a first portion of the second girder, such that the first elongate member extends in a direction approximately parallel with a second plane intersecting both of the first and second girders at another position along a length of the first and second girders; coupling the second elongate member to a second portion of the first girder and to a second portion of the second girder, such that the second elongate member extends in a direction approximately parallel with the second plane; coupling the adjustable-length jack assembly to the first portion of the first girder and to the second portion of the second girder, such that the adjustable-length jack assembly extends in a direction approximately parallel with the second plane; adjusting a length of the adjustable-length jack assembly by actuating the double-acting hydraulic jack; installing another cross-frame coupling the first and second girders together; and removing the first elongate member, the second elongate member, and the adjustable-length jack assembly from the first and second girders.
 20. The method of claim 18, wherein the first plane intersects both of the first and second girders at a location where at least one of a differential vertical deflection and a differential rotation of the first and second girders is greatest under a steel dead load with the first and second girders supported in a manner substantially identical to a cross-frame installation condition.
 21. The method of claim 18, wherein the cross-frame is designated as a first cross-frame, the first cross-frame is installed on a first side of the first plane, and a second cross-frame is installed on a second side of the first plane opposite the first side.
 22. The method of claim 18, wherein the first plane intersects both of the first and second girders at a location, and the first cross-frame is installed between the first plane and a boundary condition. 